Chapter 15, Problem 9P

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

(a) Show that when Laplace’s equation

(b) Show that when Laplace’s equation is written in spherical coordinates, it becomes

(a)

To determine

**To show:** The Laplace equation in cylindrical coordinates is

Explanation

**Given:**

The Laplace equation is

**Formula used:**

The cylindrical coordinates

The spherical coordinates

**Chain Rule:**

“Suppose that *z* where *u* is differentiable function of

**Calculation:**

From the chain rule mentioned above, it is observed that

Substitute this in the previous equation.

Differentiate this again.

Thus,

Again from the chain rule mentioned above, it is observed that

Substitute this in the previous equation.

Differentiate this again

(b)

To determine

**To show:** The Laplace equation in spherical coordinates is

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